Synthesis and Characterization of Nanofluids …
33
λ = λ M + λ E =
λ p + 2λ b f − 2φ(λ b f − λ p )
λ p + 2λb f − φ(λ b f − λ p )
+
2φε
2
r ε
2
0 U
2
0
ρν(1 + 25φ + 625φ 2 r 2 )
e
λ(T −T 0 )
(31)
The Shen’s model (2012) has been used by Bagheli et al. (2015) to predict electrical conductivity of Fe 3 O 4 nanofluid and found that it can satisfactorily predict the
electrical conductivity at lower volume fraction. However, at higher concentrations
the Shen’s model fails to predict the electrical conductivity of Fe 3 O 4 nanofluid which
is reportedly due to the agglomeration effects which are not considered in the model.
Sarojini et al. (2013) found that the Maxwell model fits well for conducting particles like Cu but not for non-conducting particles like Al 2 O 3 and CuO dispersed in
polar solvents. In fact, the Maxwell model underestimates the electrical conductivity
of Al 2 O 3 and CuO nanofluids. Same has been found by Zakaria et al. (2015) for
water/ethylene glycol mixture-based Al 2 O 3 nanofluids with ethylene glycol concentration in the basefluid above 40%. At higher ethylene glycol concentration, that is,
above 80%, there is negligible error between the experimental value and the predicted
value by the Maxwell model. Hadadian et al. (2014) studied the electrical conductivity of graphene oxide-based nanofluids and found out an equation for predicting
electrical conductivity for the sheet-like material dispersed in water. They developed
an equation for a range of temperature amongst which at 25 °C, the empirical relationship is as given in Eq. (32) having a correlation coefficient of 0.9998, where f m
is the mass fraction of the graphene oxide sheets in the nanofluid.
λ = 32.32 + 333228.571 f m
(32)
Water-based nitrogen-doped graphene nanofluids using Trixton X-100 as a surfactant for dispersion were prepared by Mehrali et al. (2015) and similar equation
was found out for determining the electrical conductivity of the nanofluid in relation
with the weight percentage (wt%) at 25 °C having a correlation coefficient of 0.999
as given in Eq. (33).
λ = 5.7471 + 1517.8 × (wt.%)
(33)
The electrical conductivity of MgO/ethylene glycol nanofluids is also incorrectly
predicted by the Maxwell as well as the Ohshima’s model as per the study of Adio
et al. (2015). Also, for Al 2 O 3 nanofluids prepared using bio-glycol/water mixtures
as basefluid, the Maxwell’s model shows similar characteristics to those obtained by
experiment but underpredicts the experimental data as found out by Abdolbaqi et al.
(2016). Shoghl et al. (2016) studied a wide range of water-based nanofluids, namely
Al 2 O 3 nanofluid, carbon nanotube (CNT) nanofluid, CuO nanofluid, MgO nanofluid,
TiO 2 nanofluid and ZnO nanofluid and found that the electrical conductivity of all
these nanofluids cannot be satisfactorily predicted by the Maxwell model. So, they
proposed new models for electrical conductivity (λ) of each nanofluid as given in
Eqs. (34), (35), (36), (37), (38) and (39), each with a correlation coefficient of 0.999,
33
λ = λ M + λ E =
λ p + 2λ b f − 2φ(λ b f − λ p )
λ p + 2λb f − φ(λ b f − λ p )
+
2φε
2
r ε
2
0 U
2
0
ρν(1 + 25φ + 625φ 2 r 2 )
e
λ(T −T 0 )
(31)
The Shen’s model (2012) has been used by Bagheli et al. (2015) to predict electrical conductivity of Fe 3 O 4 nanofluid and found that it can satisfactorily predict the
electrical conductivity at lower volume fraction. However, at higher concentrations
the Shen’s model fails to predict the electrical conductivity of Fe 3 O 4 nanofluid which
is reportedly due to the agglomeration effects which are not considered in the model.
Sarojini et al. (2013) found that the Maxwell model fits well for conducting particles like Cu but not for non-conducting particles like Al 2 O 3 and CuO dispersed in
polar solvents. In fact, the Maxwell model underestimates the electrical conductivity
of Al 2 O 3 and CuO nanofluids. Same has been found by Zakaria et al. (2015) for
water/ethylene glycol mixture-based Al 2 O 3 nanofluids with ethylene glycol concentration in the basefluid above 40%. At higher ethylene glycol concentration, that is,
above 80%, there is negligible error between the experimental value and the predicted
value by the Maxwell model. Hadadian et al. (2014) studied the electrical conductivity of graphene oxide-based nanofluids and found out an equation for predicting
electrical conductivity for the sheet-like material dispersed in water. They developed
an equation for a range of temperature amongst which at 25 °C, the empirical relationship is as given in Eq. (32) having a correlation coefficient of 0.9998, where f m
is the mass fraction of the graphene oxide sheets in the nanofluid.
λ = 32.32 + 333228.571 f m
(32)
Water-based nitrogen-doped graphene nanofluids using Trixton X-100 as a surfactant for dispersion were prepared by Mehrali et al. (2015) and similar equation
was found out for determining the electrical conductivity of the nanofluid in relation
with the weight percentage (wt%) at 25 °C having a correlation coefficient of 0.999
as given in Eq. (33).
λ = 5.7471 + 1517.8 × (wt.%)
(33)
The electrical conductivity of MgO/ethylene glycol nanofluids is also incorrectly
predicted by the Maxwell as well as the Ohshima’s model as per the study of Adio
et al. (2015). Also, for Al 2 O 3 nanofluids prepared using bio-glycol/water mixtures
as basefluid, the Maxwell’s model shows similar characteristics to those obtained by
experiment but underpredicts the experimental data as found out by Abdolbaqi et al.
(2016). Shoghl et al. (2016) studied a wide range of water-based nanofluids, namely
Al 2 O 3 nanofluid, carbon nanotube (CNT) nanofluid, CuO nanofluid, MgO nanofluid,
TiO 2 nanofluid and ZnO nanofluid and found that the electrical conductivity of all
these nanofluids cannot be satisfactorily predicted by the Maxwell model. So, they
proposed new models for electrical conductivity (λ) of each nanofluid as given in
Eqs. (34), (35), (36), (37), (38) and (39), each with a correlation coefficient of 0.999,